On the Choice of Sampling Rates in Parametric Identification of Time Series

Aliasing gives a lower bound for the sampling rate in ordinary spectral analysis of a time series. In parametric it appears at first sight that no such limitations are present. In this note we will obtain insight into this paradox by analyzing a simple Gauss-Markov process. We assume that a time series analysis is performed based on N samples of the series at equal spacing h. The result shows that there is an optimal choice of h and that the variance increases rapidly when h increases from the optimal value. The analysis of a time series of fixed length T with different number of samplings is also discussed.